International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Static Output Feedback Control Synthesis for Discrete-time T-S Fuzzy Systems

  • Dong, Jiuxiang (College of Information Science and Engineering, Northeastern University) ;
  • Yang, Guang-Hong (College of Information Science and Engineering, Northeastern University)
  • Published : 2007.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers the problem of designing static output feedback controllers for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. Based on linear matrix inequality technique, a new method is developed for designing fuzzy stabilizing controllers via static output feedback. Furthermore, the result is also extended to $H_{\infty}$ control. Examples are given to illustrate the effectiveness of the proposed methods.

Keywords

References

  1. M. Sugeno, Industrial Applications of Fuzzy Control, Elsevier, New York, 1985
  2. M. Sugeno and G. T. Nishida, 'Fuzzy control of model car,' Fuzzy Sets and Systems, vol. 16, no.1, pp. 103-113, 1985 https://doi.org/10.1016/S0165-0114(85)80011-7
  3. K. Tanaka, T. Ikeda, and H. O. Wang, 'Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H$\infty$ control theory, and linear matrix inequalities,' IEEE Trans. on Fuzzy Systems, vol. 4, no. 1, pp. 1-13, 1996 https://doi.org/10.1109/91.481840
  4. E. Kim and H. Lee, 'New approaches to relaxed quadratic stability condition of fuzzy control systems,' IEEE Trans. on Fuzzy Systems, vol. 8, no. 5, pp. 523-534, 2000 https://doi.org/10.1109/91.873576
  5. M. C. M. Teixeira, E. Assuncao, and R. G.Avellar, 'On relaxed LMI-based designs for fuzzy regulators and fuzzy observers,' IEEE Trans. on Fuzzy Systems, vol. 11, no. 5, pp. 613-622, 2003 https://doi.org/10.1109/TFUZZ.2003.817840
  6. G. Feng, C. L. Chen, D. Sun, and Y. Zhu, 'H$\infty$ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities,' IEEE Trans. on Fuzzy Systems, vol. 13, no. 1, pp. 94-103, 2005 https://doi.org/10.1109/TFUZZ.2004.839662
  7. D. W. Kim, J. B. Park, Y. H. Joo, and S. H. Kim, 'Multirate digital control for fuzzy systems LMI-based design and stability analysis,' International Journal of Control, Automation, and Systems, vol. 4, no. 4, pp. 506-515, 2006
  8. K. Tanaka, T. Hori and H. O. Wang, 'A multiple Lyapunov function approach to stabilization of fuzzy control systems,' IEEE Trans. on Fuzzy Systems, vol. 11, no. 4, pp. 582-589, 2003 https://doi.org/10.1109/TFUZZ.2003.814861
  9. D. J. Choi and P. Park, 'H$\infty$ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions,' IEEE Trans. on Fuzzy Systems, vol. 11, no. 2, pp. 271-278, 2003 https://doi.org/10.1109/TFUZZ.2003.809903
  10. H. Ohtake, K. Tanaka, and H. O. Wang, 'Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems,' IEEE Trans. on Systems, Man and Cybernetics, Part B, vol. 36, no. 1, pp.13-23, 2006 https://doi.org/10.1109/TSMCB.2005.852473
  11. Z. X. Han, G. Feng, B. L. Walcott, and J. Ma, 'Dynamic output feedback controller design for fuzzy systems,' IEEE Trans. on Systems, Man and Cybernetics, Part B, vol. 30, no. 1, pp. 204-210, 2000
  12. M. L. Lin and J.-C. Lo, 'An iterative solution to dynamic output stabilization and comments on 'Dynamic output feedback controller design for fuzzy systems',' IEEE Trans. on Systems, Man and Cybernetics, Part B, vol. 34, no. 1, pp. 679- 681, 2004 https://doi.org/10.1109/TSMCB.2002.806497
  13. H. D. Tuan, P. Apkarian, T. Narikiyo, and M. Kanota, 'New fuzzy control model and dynamic output feedback parallel distributed compensation,' IEEE Trans. on Fuzzy Systems, vol. 12, no. 1, pp. 13-21, 2004 https://doi.org/10.1109/TFUZZ.2003.819828
  14. C. L. Chen, G. Feng, D. Sun, and X. P. Guan, 'H$\infty$ output feedback control of discrete-time fuzzy systems with application to chaos control,' IEEE Trans. on Fuzzy Systems, vol. 13, no. 4, pp. 531-543, 2005 https://doi.org/10.1109/TFUZZ.2004.841732
  15. M. Johansson, A. Rantzer, and K. E. Arzen, 'Piecewise quadratic stability of fuzzy systems,' IEEE Trans. on Fuzzy Systems, vol. 7, no. 6, pp.713-722, 1999 https://doi.org/10.1109/91.811241
  16. J. Lee, C.-W. Park, H.-G. Sung, and J. Lim, 'Robust stabilization of uncertain nonlinear systems via fuzzy modeling and numerical optimization programming,' International Journal of Control, Automation, and Systems, vol. 3, no. 2, pp. 225-235, 2005
  17. C. H. Fang, Y. S. Liu, S. W. Kau, L. Hong, and C. H. Lee, 'A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems,' IEEE Trans. on Fuzzy Sysems, vol. 14, no. 3, pp. 386-397, 2006 https://doi.org/10.1109/TFUZZ.2006.876331
  18. D. Huang and S. K. Nguang, 'Robust $H_{\infty}$ static output feedback control of fuzzy systems: An ILMI approach,' IEEE Trans. on Systems, Man and Cybernetics, Part B, vol. 36, no. 1, pp. 216-222, 2006 https://doi.org/10.1109/TSMCB.2005.856145
  19. J. C. Lo and M. L. Lin, 'Robust H$\infty$ nonlinear control via fuzzy static output feedback,' IEEE Trans. on Circuits Syst. I, vol. 50, no. 11, pp.1494-1502, 2003 https://doi.org/10.1109/TCSI.2003.818623
  20. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, PA, 1994
  21. P. Gahinet, A. Nemirovski, A. J. Laub, and M.Chilali, LMI Control Toolbox, The Math Works, Natick, MA, 1995